奈特不确定下考虑红利、通涨和机制转换的最优消费投资研究

发布时间：2018-03-03 21:07

本文选题：奈特不确定性　切入点：通胀　出处：《安徽工程大学》2013年硕士论文　论文类型：学位论文

【摘要】：本文是基于Merton等众多金融研究者研究的基础上,对某些结论进行完善和推广.着重分析了在奈特不确定性环境下,股票的预期回报率服从Markov链的跨期消费和资产选择问题.具体内容分为以下三个部分：基于国内对外考虑机制转换和奈特不确定性时的最优投资组合理论研究现状,本文首先对由风险资产预期回报构成的不可观测状态下的隐马尔可夫状态转换模型做出了刻画,使人们对感性的“不可观测状态”的实际金融市场到其精确的数学模型表达有一个清晰的认识. 其次在连续时间风险模型下,假设具有递归多先验效用的投资者拥有一个不可观测的投资机会的先验集,借助Malliavin导数和随机积分方程求解投资者最优消费和投资策略的显式表达式.通过数值模拟分析时,发现不完备信息下的连续Bayes修正产生了能够削减跨期对冲需求的含糊对冲需求,含糊厌恶增大了最优投资组合策略中对冲需求的重要性.再次讨论了当市场上出现通胀因素和红利因素,上述最优投资组合结论将会发生何种变化,并对通胀因素和红利因素进行具体的量化,定量的研究不同大小的通胀和红利对最优投资组合的影响. 最后为了更好说明本文的实用性,利用蒙特·卡罗Malliavin导数模拟计算法分别说明了考虑含糊情形下最优股票需求和跨期对冲需求的变化趋势,且考虑在股票是否考虑通胀和支付红利的情况下对投资的影响.通过对模型的扩展,使得结论更加符合经济实际.
[Abstract]:This paper is based on the research of many financial researchers such as Merton to perfect and generalize some conclusions. The expected return on stocks serves the cross-period consumption and asset selection problems of the Markov chain. The specific content is divided into the following three parts:. Based on the current situation of research on optimal portfolio theory under the consideration of mechanism transformation and Knight uncertainty, this paper firstly describes the hidden Markov state transition model under the unobservable state of expected return on risk assets. So that people have a clear understanding of the perceptual "unobservable state" of the actual financial market to its precise mathematical model expression. Secondly, under the continuous time risk model, it is assumed that the investors with recursive multi-priori utility have a priori set of unobservable investment opportunities. By means of Malliavin derivative and stochastic integral equation, the explicit expression of investors' optimal consumption and investment strategy is solved. It is found that continuous Bayes correction with incomplete information leads to vague hedging demand that can reduce the intertemporal hedging demand. Vague aversion increases the importance of hedging demand in optimal portfolio strategies. This paper again discusses how the above optimal portfolio conclusions will change when inflation and dividend factors emerge in the market. The paper also quantifies the factors of inflation and dividend, and quantitatively studies the influence of different sizes of inflation and dividend on the optimal portfolio. Finally, in order to illustrate the practicability of this paper, the Monte Carlo Malliavin derivative simulation method is used to illustrate the changing trend of optimal stock demand and intertemporal hedging demand in the case of ambiguity. The paper also considers the influence of stock on investment when inflation and dividend are taken into account. Through the expansion of the model, the conclusion is more in line with the economic reality.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.59;F224

【参考文献】